Solutions for Chapter 9: Statistics for Engineers and Scientists 4th Edition

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

The mean of the conditional probability distribution of a random variable.

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

The probability mass function of the conditional probability distribution of a discrete random variable.

The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

The amount of variability exhibited by data

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

A property of a collection of events that indicates that their union equals the sample space.

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function